Non-Abelian Global Vortices

TL;DR

This paper investigates non-Abelian global vortices in the U(N) linear sigma model, revealing unique vortex solutions with irrational winding numbers in certain mass limit regimes.

Contribution

It provides numerical solutions for non-Abelian global vortices and explores their behavior in mass limit regimes, uncovering novel vortex properties.

Findings

Numerical profiles of non-Abelian global vortices are obtained.

In certain limits, vortices exhibit non-integer, irrational U(1) winding numbers.

Vortex behavior varies significantly depending on the mass hierarchy of bosons.

Abstract

We study topologically stable non-Abelian global vortices in the U(N) linear sigma model. The profile functions of the solutions are numerically obtained. We investigate the behaviour of vortices in two limits in which masses of traceless or trace parts of massive bosons are much larger than the others. In the limit that the traceless parts are much heavier, we find a somewhat bizarre vortex solution carrying a non-integer U(1) winding number 1/\sqrt{N} which is irrational in general.